## Limits Resources Continuity at a Point

Show that f(x) is continuous at x=a if and only if lim(h→0) f(a+h) = f(a).     How?

I mostly have the question of what each one is asking me to draw.   For example I have these three conditions   f(-1) = DNE limx→-1 f(x) = -2 limx→4 f(x)... Consider the following limit. lim x→2 (3x + 2) Find the limit L.

Well I know that the limit L is equal to eight. I know I get 8 by plugging in the 2 into 3x+2, but then it asks me the following:   (a) Find δ > 0 such that |f(x) − L| < 0.01... Help!! I'm stuck with this limit. Limx-->5(from the positive end) (1/ln(x-5)

I have tried using math calculators like symbolab and wolframalpha but they all cannot compute when I put the limit from the positive end. I know the answer is either 0 or DNE. But I cannot work it... What is the difference between [2, infinity) and (1, infinity)?

Don’t the both of them mean the same? i.e from 2 to infinity? There was this one mcq which had both of these options. So how do yoy differentiate between the two? FInd the 1000th derivative of Ln(x+1)

I am struggling as i know the sequence but got no idea how to describe it mathematically! What is the limit of E=n(1-Q^(1/n)) as n approaches infinity, where Q is a real number between 0 and 1?

I want an answer with Q in it if it depends on it, which I'm quite sure of. The answer to this limit (tan(πx/4)-1)/(sin(πx)) when x->1is -1/2. How to deal with Tan?

lim x->1 (tan(πx/4)-1)/(sin(πx)) Answer is -1/2 I tried to apply multiply up and down by the numerator conjugate and then don't know how to proceed. Is this even necessary? or is there...